Research proof index

Set-integral form of tendsto_truncated_vertical_shift_with_simple_pole, normalized as (2π)⁻¹ ∫ f(σ + it) dt.

Commuting evaluation with contraction. Evaluating index k and then contracting the pair i j equals contracting the corresponding pair k.succAbove i, k.succAbove j and then evaluating the residual index, up to the identity reindexing IsReindexing.succAbove_succSuccAbove_comm.

Reconstruction of a tensor from the evaluations of its last index: every t : Tensor S c is the sum over basis indices i of the evaluation evalT (Fin.last n) i t tensored with the basis covector basis ![c (Fin.last n)] (single.symm i), with the appended index permuted back into the last slot.

Basis expansion of a one-index tensor: every t : Tensor S ![c] is the sum over basis indices i of its evaluation coefficient toField (evalT 0 i t) times the corresponding basis tensor.

Reconstruction of a tensor from the evaluations of its first index: every t : Tensor S c is the sum over basis indices i of the basis covector basis ![c 0] (single.symm i) tensored with the evaluation evalT 0 i t, with the prepended index permuted back into the first slot. This is the first-index analogue of eq_sum_evalT.

Commuting evaluation with permutations.